This article about “pitch” could also be called “ear training” or “aural training”. On this page we will look uniquely at the pitch aspect of ear training. For a discussion of the rhythmic aspects of aural training click on the highlighted link. Specific pitch-reading problems related to its notation are dealt with on the following dedicated page:
Pitch: Reading and Notation Problems
Normally (but not always – see Music Reading Problems), music starts in our imagination – in our inner ear – and only then is transferred onto an instrument, voice or paper. All musicians require a highly developed “inner ear”, capable of imagining different pitches and different intervals. This “ear training is a huge part of the intellectual skills that are necessary to become a competent musician, and this is especially so for string players. With no frets, keys or valves to help us to know where we are on the fingerboard, we are often almost as dependent on our aural skills as singers are.
Being able to sing our cello parts is a very useful fundamental musical skill as well as a help to both our cello-playing and our music-reading. This skill is especially necessary in the higher fingerboard region because up there in the stratosphere, unlike in the lower (Neck and Intermediate) regions, we have no visual or mechanical references to help us to know where each note is on the fingerboard (see Positional Sense). This means that in the lower regions, we often “know” where the notes are on the fingerboard without actually needing to imagine their pitch with our “inner ear” previously, whereas in the stratosphere, if we can’t imagine the pitch of the note before we play it then we will be literally “lost in space”.
Therefore, it is especially for shifting in the Thumb Region – and most especially for larger shifts up into this region – that we usually need to have a very clear idea of the pitch of our target note, before the shift, in order to be able to do the shift with security. In other words, we need to be able to “hear” (imagine) the arrival note (or the “Intermediate Note” in the case of Assisted Shifts) with our inner ear before we start the shift. This requires good aural skills (ear training). For most shifts in (and into) Thumbposition we must find the notes almost exactly like a singer: “by ear” (with no concrete physical external reference points to help us).
Our hand can find notes in relation to physical, muscular (kinesthetic) and visual reference points but, unless we have perfect pitch, our inner ear will always find a note in relation to another previously-sounded note. Therefore the basic element of all ear training with regard to pitch is the musical interval: semitones, tones, thirds, fourths etc. We can imagine these intervals both vertically (harmonically, one note on top of the other at the same time) or horizontally (one note after the other).
HORIZONTAL AND VERTICAL HEARING
Unlike keyboard instruments, most of our time at the cello is spent playing “melodically” (or “horizontally”) in the sense that we are usually playing only one note at a time. Only when we play doublestops or chords do we actually need to imagine intervals “vertically”, hearing them simultaneously with our inner ear rather than sequentially. Therefore we will start our discussion with the “melodic” ear before progressing to the “harmonic” ear.
GETTING FAMILIAR WITH MELODIC (LINEAR, HORIZONTAL) INTERVALS
Certain intervals and series of intervals are easy to imagine with our inner ear: octaves and simple scales for example. But others are more difficult, and it is these more complex intervals and patterns that we need to work on, not initially at the cello but rather just with our inner ear: singing aloud, or singing silently in our imagination. Even some very common intervals and interval patterns can actually be quite difficult to imagine. We will look at these below.
In the same way that it helps us to better understand complex numbers if we break them up into their components (758 = [7 x 100] + [5 x 10] +[8 x 1]) we can often understand (and thus hear) complex intervals better if we “construct” them from their basic simple component intervals. For example, the diminished 7th interval is made up of 3 minor thirds piled on top of each other, while the diminished 5th is composed of two of these minor thirds.
Sometimes, especially for large intervals, rather than building an interval up from its components, it is easier to find it aurally as a simple subtraction or addition from an easily found aural reference point. In the same way that the number 999 is easiest to understand as 1000 minus 1, a major seventh is usually easiest to hear as an octave minus 1 semitone, and a major 9th as an octave + 1 tone.
In the above example, our imagining of the major 7th interval is made more difficult by the notation. Mixing sharps and flats in the same passage is like mixing up two different languages in the same sentence. It certainly makes the reading of the intervals much more complex and confusing. For more discussion of Reading (Notation) Problems click on the link.
We need to become perfectly accustomed to the different manifestations and fingerings of common intervals and interval patterns. The most difficult intervals for us to hear (imagine) are usually difficult either because of their large size or because of their “strangeness” (the most atonal or harmonically radical ones). Let’s look in more detail at some of these now. Click on the highlighted links for practice material (exercises and repertoire excerpts). We will start with the smallest intervals and work upwards.
SEMITONES: CHROMATIC SCALES
On this page, we are looking at the problems of hearing chromatic scales. The intellectual problems of reading them, and the physical problems of playing them, are dealt with on separate pages.
Unless they are played quite slowly, we will not be able to control (imagine) every note of a chromatic scale (see Control – Overcontrol). We need instead to have just a few reference points during the scale. These reference points will be determined almost certainly by the rhythm, and will probably be the notes that fall on the strong beats. Sometimes this makes our job easy, as in triplet rhythms which divide a chromatic scale into a series of minor thirds, giving us the diminished 7th arpeggio:
When however a chromatic scale comes in binary groupings, then the octave is made up of three major thirds (instead of four minor thirds). This is much harder for us to hear with our inner ear, especially when the shifts don’t coincide with the strong beats.
The following link opens up two pages of exercises that will train our ear to hear better (and therefore be better able to control) chromatic scales on the same string(s). In these exercises we use the open strings to check our intonation at various points in the chromatic scales:
Pitch Control Exercises For Chromatic Scales On the Same String: Double-stops
Normal chromatic scales do not pose a reading problem, because we know that every interval is a semitone. Serious reading problems are however posed by irregular chromatic passages because we need to decode each interval separately. Click on the highlighted link for more about this.
“STRANGE” SCALES AND MODES
We are normally so used to the major and minor scales that they do not present us with any aural difficulties: we can sing them up and down with absolutely no problems. Other more unusual scales (modes) require more work (practice) to feel familiar. We normally practice/sing our major and minor scales starting on the tonic. If we practice starting them on other notes of the scale then we will be effectively accustoming ourselves to all the different modes.
THE MINOR THIRD AND DIMINISHED SEVENTH CHORDS
The minor third is normally an easy interval to imagine even in the most difficult harmonic circumstances, and it is often an extremely useful interval with which to break up (subdivide) larger complex intervals. For example, the minor third is the most tonally-useful common denominator of the octave. Whereas an octave divided in half gives two augmented fourths (or diminished fifths) which can be quite hard to imagine with our inner ear, the octave divided into quarters gives four minor thirds, which are very easy to imagine. So in any series of consecutive minor thirds, the fifth one will be the octave of the first one.
While semitones and tones are the building blocks of all our different scalic progressions, with the minor third we make a quantum leap into the totally new world of harmony. The minor third is a basic harmonic building block, not only of the major and minor chords but also of the important diminished seventh chord, which is composed of three minor third intervals piled on top of each other. This chord is both very expressive and extremely versatile: by lowering any one of its notes by a semitone, that new note becomes the bass of a dominant seventh chord, permitting a modulation. This makes it a very popular, much-used harmonic and melodic device, so we really need to have its intervals very well ingrained into our ears. On the cello, we have two basic standard diminished seventh chord configurations across three strings. These can be moved all over the fingerboard:
Sibelius writes us a little study for these two finger configurations in his Third Symphony:
Here below are links to practice material featuring these useful and important piles of minor thirds:
Diminished Seventh Chords: EXERCISES Diminished Seventh Chords: REPERTOIRE EXCERPTS
AUGMENTED FOURTHS/DIMINISHED FIFTHS
Although these two intervals are exactly the same distance apart, we “hear” them differently, in the sense that the “intermediate notes” (those occurring between the starting and finishing points) are quite different for the two intervals. We will normally hear the diminished 5th as the sum of two minor thirds, whereas to hear the augmented fourth we will probably use the whole tone scale as stepping-stones. Because this augmented fourth interval is made up of three tones, it is also called the “tritone”:
We are very accustomed to diminished fifths because, being part of the diminished seventh chord, they are found very frequently. Augmented fourths however, even though they occur between the fourth and seventh notes of every standard major scale (and between the third and sixth note of any melodic minor scale), are still somewhat unusual as a melodic interval and may cause us more aural (pitching) problems than the diminished fifth.
Here are some augmented fourths from the repertoire:
Sometimes we can choose how we want to “hear” the interval: either as a diminished fifth or as a tritone (augmented fourth). This choice may be reflected in our choice of intermediate notes:
THE DIMINISHED SEVENTH INTERVAL
The diminished seventh interval is a curious one because not only does it sound the same as the major sixth, it is also normally notated identically. So why is it called a diminished seventh? ….. because just like for the above example (the augmented fourth and its identical diminished fifth), we hear the two identical intervals differently. In imagining the major sixth we will use quite different aural stepping-stones to the layered minor thirds that we will use for the diminished seventh.
MINOR SEVENTH INTERVAL (AND DOMINANT SEVENTH ARPEGGIOS)
We can “hear” (find) this interval in two main ways:
- by imagining a note one octave higher, and then going down a tone, or
- by imagining the stepping-stones of the dominant seventh arpeggio (major third + two minor thirds)
FINDING THE BASIC INTERVALS IN A COMPLEX PASSAGE
Often a quite simple passage can be made to seem more complex than it really is due to the presence of chromatic “ornamentations” which produce some strange (hard-to-sing) intervals. It helps a lot in learning these passages if we can see and practice the underlying basic interval structure.
And here is another repertoire example of this procedure, this time with a diminished 7th chord as the basic structure that we need to hear:
Knowledge and awareness of the harmony underneath an awkward interval or passage will usually help us to better hear it with our inner ear (and thus find it on the fingerboard). Very often it is only when we can imagine (or hear) the harmonic accompaniment, that the melodic interval will suddenly make musical sense.
COUNTERPOINT AND DOUBLE-STOPS: SEPARATING THE VOICES
For good control and intonation in our doublestopped passages, we need to be able to clearly separate the two voices with our ears. This can be quite difficult at first because we spend so much of our playing time just hearing and tuning one note. In most of our music-making the “other note” is played by another instrument and we don’t have to worry about it because it is beyond our control, but in double-stops, suddenly, we need to control two notes simultaneously. Playing and practising double-stops forces us to develop this aural skill. Perhaps the best way to develop this aural skill quickly and efficiently is to practice singing one of the voices while sounding only the other voice with the cello.
The following link opens up two pages of doublestoppped scales in thirds and sixths which we can use as material for developing this skill. While the left-hand “plays” on both strings, the bow plays only the line that we are not singing. We will probably discover that it is much easier to hear (and sing) the top line of any doublestopped passage and that therefore we may need to spend more time singing its the lower line.
Play One Voice While Singing The Other
THE SINGING CELLIST
Singing one voice while simultaneously playing another different musical line (voice) is an excellent way to develop our aural (inner hearing) skills. This subject has its own dedicated page: